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Article Content:-
Abstract
The main aim of this research is to find the formula of the trace of adjacency matrix from a cycle graph to the power of six to ten. The first step to obtain the general form is finding the general formula of adjacency matrix from a cycle graph to the power of six to ten. Furthermore, the formula of that trace of adjacency matrix obtained and proven by direct proof. We also present an implementation of the formula by an example.
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References
C. Brezinski, P. Fika, dan M. Mitrouli, “Estimations of the Trace of Powers of Positive Self-Adjoint Operators by Extrapolation of the Moments,” Electronic Transactions on Numerical Analysis, vol. 39, hal. 144–155, 2012.
J. Pahade dan M. Jha, “Trace of Positive Integer Power of Real 2 × 2 Matrices,” Advances in Linear Algebra & Matrix Theory, vol. 5, no. 04, hal. 150, 2015.
F. Aryani dan M. Solihin, “Trace Matriks Real Berpangkat Bilangan Bulat Negatif,” Jurnal Sains Matematika dan Statistika, vol. 3, no. 2, hal. 16–23, 2017.
F. Aryani dan Y. Yulianis, “Trace Matriks Berbentuk Khusus 2 × 2 Berpangkat Bilangan Bulat Negatif,” Jurnal Sains Matematika dan Statistika, vol. 4, no. 2, hal. 105–113, 2018.
F. Aryani dan N. Husna, “Trace Matriks Toepitz Tridiagonal 3 × 3 Berpangkat Bilangan bulat Positif,” Jurnal Sains Matematika dan Statistika, vol. 5, no. 1, hal. 40–49, 2019.
R. Rahmawati, N. A. Putri, F. Aryani, dan A. N. Rahma, “Trace Matriks Toeplitz Simetris Bentuk Khusus Ordo 3 × 3 Berpangkat Bilangan Bulat Positif,” Jurnal Sains Matematika dan Statistika, vol. 5, no. 2, hal. 61–70, 2019.
F. Aryani, D. R. Sari, C. C. Marzuki, dan S. Gemawati, “Trace Matriks Toeplitz Kompleks Khusus Ukuran 3 × 3 Berpangkat Bilangan Bulat Positif,” in Seminar Nasional Teknologi Informasi, Komunikasi dan Industri, 2018, hal. 673–681.
F. Aryani, C. Anam, dan C. C. Marzuki, “Trace Matriks Kompleks Berbentuk Khusus 3 X 3 Berpangkat Bilangan Bulat,” Jurnal Sains Matematika dan Statistika, vol. 6, no. 1, hal. 122–132, 2020.
F. Aryani, R. Andesta, dan C. C. Marzuki, “Trace Matriks Berbentuk Khusus 3×3 Berpangkat Bilangan Bulat Positif,” Jurnal Sains Matematika dan Statistika, vol. 6, no. 1, hal. 40–49, 2020.
F. Aryani dan R. Taslim, “Trace Matriks 3 x 3 Berpangkat Bilangan Bulat,” Jurnal Sains Matematika dan Statistika, vol. 7, no. 1, hal. 1–9, 2021.
Rahmawati, N. A. Putri, F. Aryani, dan A. N. Rahma, “Trace Matriks Toeplitz Simetris Bentuk Khusus Ordo 3×3 Berpangkat Bilangan Bulat Positif,” Jurnal Sains Matematika dan Statistika, vol. 5, no. 2, 2019.
J. K. Pahade dan M. Jha, “Trace of Positive Integer Power of Adjacency Matrix,” Global Journal of Pure and Applied Mathematics, vol. 13, no. 6, 2017.
F. Aryani, A. A. Nugraha, M. Faisal, dan C. C. Marzuki, “Trace Matriks Ketetanggaan n × n Berpangkat -2, -3, -4,” Proceding SNTIKI 12, hal. 543–553, 2020.
K. H. Rosen, Discrete Mathematics and Its Applications. New York: Mc Graw Hill, 2019.
F. Aryani, D. A. Puspita, C.C. Marzuki, Y. Muda, "Trace of the Adjacency Matrix